Question

1. find the measure of ∠1.

a. 65°
b. 55°
c. 25°
d. 115°
e. 75°

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \((5x - 10)^{\circ}=40^{\circ}+3x^{\circ}\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find the measure of \(\angle1\)

Since \(\angle1+(5x - 10)^{\circ}=180^{\circ}\) (linear pair), substitute \(x = 25\) into \((5x - 10)^{\circ}\). First, \((5x - 10)^{\circ}=(5\times25-10)^{\circ}=(125 - 10)^{\circ}=115^{\circ}\). Then \(\angle1=180^{\circ}-(5x - 10)^{\circ}\). Substitute \(x = 25\) again, \(\angle1=180^{\circ}-115^{\circ}=65^{\circ}\)

Answer:

A. \(65^{\circ}\)